DeepTOFSino: A deep learning model for synthesizing full-dose time-of-flight bin sinograms from their corresponding low-dose

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Article

Reference

DeepTOFSino: A deep learning model for synthesizing full-dose time-of-flight bin sinograms from their corresponding low-dose

sinograms

SANAAT, Amirhossein, et al .

Abstract

Purpose: Reducing the injected activity and/or the scanning time is a desirable goal to minimize radiation exposure and maximize patients' comfort. To achieve this goal, we developed a deep neural network (DNN) model for synthesizing full-dose (FD) time-of-flight (TOF) bin sinograms from their corresponding fast/low-dose (LD) TOF bin sinograms.

SANAAT, Amirhossein, et al . DeepTOFSino: A deep learning model for synthesizing full-dose time-of-flight bin sinograms from their corresponding low-dose sinograms. NeuroImage , 2021, vol. 245, p. 118697

DOI : 10.1016/j.neuroimage.2021.118697 PMID : 34742941

Available at:

http://archive-ouverte.unige.ch/unige:156377

Disclaimer: layout of this document may differ from the published version.

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ContentslistsavailableatScienceDirect

NeuroImage

journalhomepage:www.elsevier.com/locate/neuroimage

DeepTOFSino: A deep learning model for synthesizing full-dose

time-of-ﬂight bin sinograms from their corresponding low-dose sinograms

Amirhossein Sanaat

^a

, Hossein Shooli

^b

, Sohrab Ferdowsi

^c

, Isaac Shiri

^a

, Hossein Arabi

^a

, Habib Zaidi

^a^,^d^,^e^,^f^,^∗

aDivision of Nuclear Medicine and Molecular Imaging, Geneva University Hospital, Geneva, Switzerland

bPersian Gulf Nuclear Medicine Research Center, Department of Molecular Imaging and Radionuclide Therapy (MIRT), Bushehr Medical University Hospital, Faculty of Medicine, Bushehr University of Medical Sciences, Bushehr, Iran

cUniversity of Applied Sciences and Arts of Western, Geneva, Switzerland

dGeneva University Neurocenter, University of Geneva, Geneva, Switzerland

eDepartment of Nuclear Medicine and Molecular Imaging, University of Groningen, Groningen, Netherlands

fDepartment of Nuclear Medicine, University of Southern Denmark, Odense, Denmark

a r t i c le i n f o

Keywords:

PET/CT Brain imaging Low-dose imaging Deep learning Time-of-ﬂight

a b s t r a ct

Purpose: Reducingtheinjectedactivityand/orthescanningtimeisadesirablegoaltominimizeradiationexpo- sureandmaximizepatients’comfort.Toachievethisgoal,wedevelopedadeepneuralnetwork(DNN)modelfor synthesizingfull-dose(FD)time-of-ﬂight(TOF)binsinogramsfromtheircorrespondingfast/low-dose(LD)TOF binsinograms.

Methods: ClinicalbrainPET/CTrawdataof140normalandabnormalpatientswereemployedtocreateLDand FDTOFbinsinograms.TheLDTOFsinogramswerecreatedthrough5%undersamplingofFDlist-modePET data.TheTOFsinogramsweresplitintoseventimebins(0,±1,±2,±3).Residualnetwork(ResNet)algorithms weretrainedseparatelytogenerateFDbinsfromLDbins.AnextraResNetmodelwastrainedtosynthesizeFD imagesfromLDimagestocomparetheperformanceofDNNinsinogramspace(SS)vsimplementationinimage space(IS).Comprehensivequantitativeandstatisticalanalysiswasperformedtoassesstheperformanceofthe proposedmodelusingestablishedquantitativemetrics,includingthepeaksignal-to-noiseratio(PSNR),structural similarityindexmetric(SSIM)region-wisestandardizeduptakevalue(SUV)biasandstatisticalanalysisfor83 brainregions.

Results: SSIMandPSNRvaluesof0.97±0.01,0.98±0.01and33.70±0.32,39.36±0.21wereobtainedforIS andSS,respectively,comparedto0.86±0.02and31.12±0.22forreferenceLDimages.Theabsoluteaverage SUVbiaswas0.96±0.95%and1.40±0.72%forSSandISimplementations,respectively.Thejointhistogram analysisrevealedthelowestmeansquareerror(MSE)andhighestcorrelation(R² =0.99,MSE=0.019)was achievedbySScomparedtoIS(R²=0.97,MSE=0.028).TheBland&Altmananalysisshowedthatthelowest SUVbias(-0.4%)andminimumvariance(95%CI:-2.6%,+1.9%)wereachievedbySSimages.Thevoxel-wise t-testanalysisrevealedthepresenceofvoxelswithstatisticallysigniﬁcantlylowervaluesinLD,IS,andSSimages comparedtoFDimagesrespectively.

Conclusion: TheresultsdemonstratedthatimagesreconstructedfromthepredictedTOFFDsinogramsusingthe SSapproachledtohigherimagequalityandlowerbiascomparedtoimagespredictedfromLDimages.

1. Introduction

Non-invasivefunctionalimagingusingpositronemissiontomogra- phy(PET)istheultimatetechniqueforthevisualizationandquantiﬁ-

PET,PositronEmissionTomography;DNN,DeepNeuralNetworks;LD,Low-dose;FD,Full-dose;ResNet,Residualnetwork;TOF,Time-of-Flight;SNR,Signal- to-NoiseRatio;OP-OSEM,Poissonorderedsubsets-expectationmaximization;SSIM,StructuralSimilarityIndexMetric;RMSE,RootMeanSquaredError;SUV, StandardizedUptakeValue;STD,standarddeviation;IS,ImageSpace;SS,SinogramSpace.

∗Correspondingauthorat:GenevaUniversityHospital,DivisionofNuclearMedicineandMolecularImaging,CH-1211Geneva,Switzerland.

E-mailaddress:[email protected](H.Zaidi).

cationofeventsatthecellularandmolecularlevels.PETiswidelyused fortheassessmentofneurodegenerativediseases andotherneurolog- icaldisorders(Zaidietal.,2010).PETreconstructionalgorithmsgen- erateathree-dimensional(3D)imagerepresentingtheradiotracerdis-

https://doi.org/10.1016/j.neuroimage.2021.118697.

Received4July2021;Receivedinrevisedform21September2021;Accepted29October2021 Availableonline4November2021.

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A. Sanaat, H. Shooli, S. Ferdowsi et al. NeuroImage 245 (2021) 118697

tributionwithinthebody,providingusefulinformationaboutbiolog- icalprocesses invivo.PETisarelativelynoisyimagingmodalityow- ingtothelowstatisticsoftheacquiredeventsandthePoissonnature ofannihilationphotonsemissionanddetectionprocesses.Thetechni- calaspects,includingPETscanner’sgeometry,photodetectiontechnol- ogy,reconstructionmethodology,alongwithphysiologicalconsidera- tions,suchaspatientmotion(particularlyforpatientssufferingfrom dementiathat aremore susceptibletoinvoluntarymotion)influence thequalityandquantitativeaccuracyofPETimages.Furthermore,the numberofcollectedtrueevents,whichhasadirectrelationshiptothe scanning/acquisitiontimeandamountofinjectedradiotracer,impacts PETimagequality.Increasingthescanningtimecausesadditionaldis- comforttoelderlyandpediatricpatientsanddecreasesthescanner’s throughput.Conversely,increasingtheamountofinjectedradiotracer facesconcernswithrespecttopotentialradiationhazards,particularly inchildrenandpatientsundergoingmultiplePETexaminationsatdif- ferenttimeintervalsforfollow-upormonitoringoftreatmentresponse (Arabietal.,2021;Sanaatetal.,2021).Reducingtheinjectedactivityor scanningtimehampersimagequalityanddecreasesthesignal-to-noise ratio(SNR),whichmightjeopardizeclinicaldiagnosisandbiasedquan- tification.Hence,techniquesenablingtoreducetheinjectedactivityor scanningtimewhilemaintainingtheclinicalinformationofPETimages similartostandarddosescansarehighlydesired.

Inrecent years,a plethora of deep neuralnetworks (DNN)were proposedtoaddresstheissueofnoisereductionandimprovementof image qualityin low-dose (LD)PET imaging while preserving clini- calinformation(ZaidiandElNaqa,2021).Artificialintelligencealgo- rithmsareblackboxtechniquesthatcanlearnanytypeofnonlinear transformationforalargenumberoftasks,specificallyintheimage- to-imagetranslationdomain.Duringthelastdecade,anumberofDNN modelsweredevelopedforimage-to-imagetranslation,demonstrating reasonableperformancein directPET imagereconstructionmapping therepresentationsfrommulti-modalimages,suchasdatafromsino- gramtoimagedomains(Häggströmetal.,2019;Sanaatetal.,2020; SanaatandZaidi,2020),cross-modalitymultisequenceMRtoPETcon- version(Weietal.,2020),generationofsyntheticCTfromMRimages (Arabi et al., 2019; Han, 2017), internal radiation dosimetrywhere CTandPETimagesarefedinto themodeltopredict thedosemap (Akhavanallafetal.,2021),synthesizingPET/CTattenuationcorrected fromnon-attenuatedcorrectedimages(Arabietal.,2020;Yangetal., 2019), and image denoising (Chen et al., 2019; Kang et al., 2015; Kaplanand Zhu,2019; Ouyang etal., 2019; Schaefferkoetter et al., 2017;Wangetal.,2018;Xiangetal.,2017).

VariousPETimagedenoisingtechniquesusingDNNsinimagespace werereported.Forinstance,Chenetal.adoptedaresidualU-Netarchi- tectureforestimatingthefull-dose(FD)imagesfromanLDwith200th dosereduction(Xuetal.,2017).Othergroupsexploredthepossibility ofusinganatomicalinformationfromconcurrentimagingmodalities, suchasCTorMRIindenoisingprocesstoenhancethesynthesizedFD PETimagequality.Inthisregard,Chenetal.usedaU-Netmodelin- corporatingMR sequences(T1,T2-weighted,andT2-FLAIR)intothe learningprocesstoestimateFD¹⁸F-FlorbetabenbrainPETimagesfrom LDimagesto1%ofthecorrespondingacquisitiontimeofFDimages (Chenetal.,2019).

Mostprevious studiesusing deep learning-guidedPET imagede- noising in theimagedomain. One of thedisadvantages of using re- constructedimagesisthatthemodelsaretrainedforaspecificclini- calprotocol,whichlimitstheapplicabilityofthemodeltothespecific reconstructionprotocoladopted(parameters,post-reconstructionfilter- ing,etc.).Hence,switchingtoadifferentclinicalprotocolentailsretrain- ingagaintheDNNmodel.Conversely,thepredictionofFDsinogramsin theprojectiondomainmakesitpossibletoapplyvariousimagerecon- structionprotocols.Suchanapproachwasadoptedinourrecentwork wherewedevelopedtwo U-Netmodels:oneconventional tosynthe- sizeFDimagesfromLDimagesandanothertosynthesizeFDnon-time- of-flight(TOF)sinogramsfromLDnon-TOFsinograms(Sanaatetal.,

2020).The comparisonof these twoapproachesprovedthat FDim- agesreconstructedfromthepredictedsinogramseﬀectivelyreducedthe noiselevelandexhibitedsuperiorperformanceintermsofimagequal- ityandquantitativeaccuracy.Hongetal.(2018)proposedadeepresid- ualsinogramsuper-resolutionnetworktoimprovethequalityofimages producedbyaPETscannerequippedwithlargepixelatedcrystals.They trainedtheirmodelusingsinogramsfromascannerwiththincrystals, togeneratehigh-resolutionsinograms.Furthermore,morerecentwork reportedonpriorknowledge-drivenDNN-basedapproachforsinogram denoising(Luetal.,2020).

TOFPETimagingprovideshighersignal-to-noiseratioandoverall improvedimagequalitycomparedtononTOFPET,particularlyforlarge objects(Surti,2015).Thisenablesfaster/lowerdosePETimaging.Inthis regard,denoisingtheTOFPETdatainthesinogramdomainishighly desiredtotakefulladvantageofthepotentialofTOFPETimaging.

Oneofthelimitationsofourabovereferencedpreviousworkisthat TOFwasnotconsidered,andassuch,thetechniquewasnotexploited toitsfullpotential(Sanaatetal.,2020).Inthiswork,wesetouttode- velopamodelconsistingofsevenResidualnetwork(ResNet)architec- turestopredictsevenFDsinogramscorrespondingtovariousTOFbins (0,±1,±2,±3)fromtheircorrespondingLDTOFbinsinogramsinan end-to-endfashion.Thereafter,thegeneratedTOFsinogramscouldbe reconstructedusinganyPETimagereconstructionalgorithm.Weused diﬀerentResNetmodelsfortrainingthenetworkinimagespace.The synthesizedimagesderivedusingbothmethodologies(imagespaceand sinogramspace)werethencompared.

2. Materialsandmethods 2.1. PET/CTdataacquisition

Thecurrentstudywascarriedoutusingadatabaseconsistingof140

18F-FDGbrainPET/CTstudiescollectedbetweenJune2017andMay 2019atGenevaUniversityHospital.Thedatasetcoversawiderange ofpatientswithcognitivesymptomsofpossibleneurodegenerativedis- eases.Thepatientsconsistedof66males(73±9yrs)and74females (72±11yrs).Thedemographicinformationofpatientsissummarized inTable1.Thestudyprotocolwasacceptedbytheinstitution’sethics committeeandallpatientsgavewritteninformedcontent.List-mode datawereacquiredonaBiographmCTscanner(SiemensHealthineers, Erlangen,Germany)about35minpost-injection. Alow-doseCTscan (120kVp,20 mAs)wasperformedforPET attenuationcorrection.A standardimagingprotocolconsistingof20minscanningtimefollow- ingtheinjectionof205±10MBqof¹⁸F-FDG.PETlist-modedatawere firstbinnedintosinogramsandthenreconstructedusingthee7tools offlinereconstructiontoolkit(SiemensHealthcare).Anextensionofthis toolkit,referredtoas“decimate.js”,enablestoproducerandomlyun- dersampledTOFsinogramscorrespondingtoapredefinedpercentageof thetotalnumberofcollectedevents,thusallowingtogeneratelow-dose scansfromfull-dosescans.EachproducedTOFsinogramhasamatrix sizeof400×168×621×13,withthefourthdimensionrepresenting thenumberoftimebinsfortheBiographmCThavingaTOFcoincidence timeresolutionof∼530ps(0,±1,±2,±3,±4,±5,±6).Sincethehead isalwayspositionedinthecenterofthefield-of-viewandgiventhatthe sizeofthehead,itiscommonlycontainedwithinonly7bins(0,±1,

±2,±3).Hence,wetrained7modelscorrespondingtothesetimebins.

Arandomsubsetcontaining5%ofthetotaleventswasextractedfrom thelist-modedatatoproduceaLDTOFsinogram.AnordinaryPoisson orderedsubsets-expectationmaximization (OP-OSEM)algorithmcon- sideringTOFandpointspreadfunctionmodelingwith5iterationsand 21subsetswasusedforreconstructionofbothFDandLDPETimages withamatrixsizeof200×200×109and2.03×2.03×2.2mm³voxel size.Gaussianpost-reconstructionﬁlteringwith2mmFWHMwasap- plied.

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Table1

Demographicinformationofpatientsincludedinthisstudy.

Training Test Validation

Number 100 30 10

Male/Female 45/55 15/15 4/6 Age (Mean ± SD) 73 ± 8 71 ± 16 69 ± 7.5

Indication/Diagnosis Cognitive symptoms of possible neurodegenerative an etiology

Fig.1.AschematicoftheResNetnetworkusedinthiswork.Insevenseparatestepslowdosesinogramstimebins(−3,−2,−1,0,1,2,3)werefedin7separateResNet modelsasinputandfulldosesinogramsbelongtoeachtimebinpredicted.Inimagespacetrainingphase,wefedaResNetmodelwithTOFLDimagestopredict TOFFDimages.

2.2. ResNetarchitecture

ThecoreelementtoanyResNETistheresidualblockoriginallypro- posedin(Heetal.,2016)alongwithitslatervariants.Theresidualcon- nectioncircumventsthemanyissuesfacedwhileincreasingthenum- beroflayersofneuralnetworksandeﬃcientlyfacilitatestrainingvery deepnetworks.Thishasrevolutionizedthedeeplearningpracticeacross manydisciplines,includingtheapplicationtargetedinthiswork,i.e., image-to-imagetranslation.

AgeneraldescriptionofaresidualconnectionisdepictedinFig.1. Let𝑓_𝜃^[^𝑙](⋅)the𝑙^thmoduleofaDNN,where𝑙=1,⋯,𝐿and𝜃symboliz- ingthesetofalllearnableparametersoftheneuralnetwork,whichare updatedduringtraining.Thisusuallyconsistsofacoupleofconvolu- tionallayerswithReLUnon-linearitiesinbetween.Let𝐱^[^𝑙⁻¹^]denotethe inputtothisconvolutionalmodule,where𝐱^[0]=𝐱istheinputimage.

Theresidualblockproducestheoutputasfollows:

𝐱^[^𝑙^]=𝐱^[^𝑙−1^]+𝑓_𝜃^[^𝑙^]( 𝐱^[^𝑙−1^])

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whichisthenfedtothenextblock.Thishasmanybenefits,including thefactthatthenetworkwillhavethepossibilitytocircumventamod- uleifitslowsdowntheoptimization,e.g.,duetoexplodingorvanishing gradientissues(Xieetal.,2017).Moreover,fromtheperspectiveofcon- volution,itprovidesadiversesetofeffectivereceptivefields.

Thisbasicideaisthenappliedinvariouswaysusingmodernnet- works.U-Netprovedtobeasuccessfulconceptinimage-to-imagetrans- lationandisverypopularinthemedicalimageprocessingandanalysis domains(Huangetal.,2017).ConsiderasimpliﬁedstructureofaU- Netwith3leftmodules𝑓_↓^[^𝑙](⋅),aswellas3rightmodules𝑓_↑^[^𝑙](⋅).The outputofanyleftmoduleisdownsampledandfedtothenextleftmod- ule,inadditiontobeingdirectlyfedintoitscorrespondingrightmodule, whichalsoreceivesup-sampledsignalsfromthepreviousrightmodule.

Therefore,theﬁnaloutputisformedas:

𝐱^[^𝐿^]=𝑓_↑^[^𝐿^]( 𝑓_↓^[¹^](

𝐱^[⁰^]) +𝐱^[^𝐿⁻¹^])

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Hencetheoutputimagegetsdirectlyasignalfromtheﬁrstlayer.

Whilethis issuccessful inmany tasks(e.g.image segmentation),for taskswheretheinput-outputimagepairsareverysimilarlikeinauto- encoding,thenetworkusestheeasierdirectpathwayfromtheinputto theoutput.Atrialanderrorexerciserevealedthatnomatterhowmany modulesexistintheU-Net,insuchcases,thesignaldoesnotpropagate throughthemandtheoutputreliesmostlyontheﬁrstmodule.

Inourcase,wherethelow-doseandfull-doseimagesaresomehow similar,wenoticedthisphenomenonbynotachievingsatisfactoryre- sults.ThisledustochosemoresequentialResNetvariants.Inparticular, weadoptedtheResNetstructureproposedin(Ronnebergeretal.,2015) depictedinFig.1,alsoimplementedinNiftyNet(Gibsonetal.,2018).

Thisnetworkhasarelativelysimpleresidualstructureandavoids down-samplingandup-samplingoperations,whichcomplicatestheim- plementationprocess(Lietal.,2017).Instead,itmakesextensiveuseof dilatedconvolutionsthatincreaseeffectivelythereceptivefieldofthe network,sothatitlearnslongerrangeentitiesintheimage.Another verywell-knownelementinthisnetworkisbatch-normalizationwhose combinationwithresidualconnectionshasbecomeastandardandvery effectiverecipetospeed-upthetrainingofdeepmodels.

Eachoftheﬁrst19modulesofthenetworkexclusivelyusesconvo- lutionalkernelsofsize3×3×3,alongwithbatch-normalizationand ReLU.Intheﬁrst7modules,thenetworkuses16ofthesekernels,the following6modulesuse32kernels,butwithadilationparameterof2, andthenext6modulesuse64kernelswithdilation4.Thelastlayer consistsofaconvolutionalkernelofsize1×1×1toadjustthenumber ofoutputlayerstothoseofthehigh-doseimages.

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We used the simple squared l₂ loss function for training, i.e., 𝑙(𝐱_𝑖,𝐱_𝑜)=||𝐱_𝑖−𝐱_𝑜)||²₂ forbothofthepixelandprojectiondomains.If youusel₂,youshoulddeactivate softmax.Thenetworkwastrained andtestedusingNVIDIA2080TiGPUwith11GBrandomaccessmem- oryrunningunderwindows10.Thetrainingwasperformed for300 epochs.Thetrainingandvalidationof thenetworkwasperformedon 110patients,whileaseparateunseendatasetof30patientsservedas thetestdataset.

2.3. Evaluationstrategy

2.3.1. Quantitativeanalysis

For estimation of the accuracy of our DNN models, three well- established quantitativemetrics, including peak signal-to-noise ratio (PSNR),structuralsimilarityindex metric(SSIM)andtherootmean squarederror(RMSE)wereusedtocompareISandSSimplementations withFD.Moreover,tohaveaninsightaboutthelevelofSNRinLDim- agesandﬁgureouthowmuchResNetcanincreaseSNR,thesemetrics werealsocalculatedfortheLDimages.

Thestandardizeduptakevalues(SUVs)andtheirstandarddeviations (STDs)wereestimatedfor83brainregionstoevaluatethequantitative accuracybetweenreferenceFD,LD,andsynthesizedimages(ISandSS) images.Theregion-wiseanalysiswasperformedusingPMODmedical imageanalysissoftware(PMODTechnologiesLLC,Switzerland)bycon- sideringabrainatlasconsistingof15 malesand15femaleswithan averageageof31years(Hammersmithatlasn30r83).

Ajointhistogramanalysiswascarriedouttoassessvoxel-wisethe correlationbetweentheactivityconcentrationingroundtruthFDand LD,andIS andSS images.Inaddition,Bland& Altmananalysisand folded empiricalcumulativedistributionplot orMountain plotwere drawntocomparethedistributionofregions’SUVsfordiﬀerentregions betweenthereferenceandsynthesizedimages. Amountainplotwas generatedbycalculationofapercentileforLD,IS,SSimagesandref- erenceFDimages.Inthisplot,thevariationbetweenthetwoimagesis depictedonthelengthoftails.ToevaluatetheRMSE,SSIM,andPSNR metrics,statisticalanalysisusingpairwiset-testwasperformedbetween ISvsSS,ISvsLD,andSSimages.Forallcomparisons,thethresholdof statisticalsigniﬁcancewassetat5%.

2.3.2. Statisticalanalysis

Original FD,LD, ISand SS imageswerepre-processed using FSL (FMRIBSoftwareLibraryv6.0.1,AnalysisGroup,FMRIB,Oxford,UK).

Firstly,theHammersmithatlaswasregisteredtoan¹⁸F-FDGbrainPET template(inMontrealNeurologicalInstitutestandardspace)using12- affinetransformationregistrationusingFLIRT(FMRIB’sLinearImage RegistrationTool).Subsequently,non-brainregionsoftheatlas(cere- bellumandbrainstem)wereexcludedandbinarizedtocreateaHam- mersmithatlas-basedbrainmask.Then,allFDimageswereregistered tothe¹⁸F-FDGPETtemplatewith12-affinetransformationregistration usingFLIRT.Afterwards,LD,IS,andSSimagesofeachsubjectwerereg- isteredtothetemplateviaFLIRTusingthesametransformationmatrix usedinFDimageregistrationstepforthatsubject.Finally,allFD,LD,IS, andSSimagesweremaskedusingthebrainmasktoexcludenon-brain regionsinall images.Weapplied alinearimageregistrationmethod thatdonotchangevoxel’svalueswithoutsmoothingtominimizeeffect ofpre-processingontheresults.

Afterpre-processingsteps, amassunivariatemethodologyof Sta- tisticalParametricMapping(SPM12;WelcomeCentreforHumanNeu- roimaging,UCL,UK)wasusedtoconductavoxel-by-voxeltwo-sample t-testcomparingvoxelwiseFDimageswiththecorresponding LD,IS, andSSimages(FDvsLD,FDvsIS,andFDvsSS)(Fristonetal.,1994).

Thisanalysisidentifiesvoxelswithsignificantdifferencewithrespectto FDimages.Statisticalsignificancewasdefinedatavoxel-wisethreshold (family-wiseerrorcorrectedp<0.05)andnoextentthresholdofcontigu- ousvoxelswasdefined.Inaddition,thenumber,percentage,andlevel

Fig.2. ¹⁸F-FDGbrainPETimagesofa71-year-oldfemalepatientwithcog- nitivesymptomsofpossibleneurodegenerativeetiologyshowing(a)theTOF full-doseimageusedasreferenceand(b)low-doseTOFPETimage.(c)The predictedstandarddosePETimagesinimagespaceshowsigniﬁcantlyreduced noisecomparedwithlow-dosePETimages,whiletheimagesgeneratedfrom sinogramspace(d)weresuperiorinreﬂectingtheanatomicalfeatures.Thebias mapforlowdoseandpredictedimagesinimagespaceandsinogramspacewith respecttoFDimagesareillustratedin(e),(f),and(g),respectively.

ofsigniﬁcance(T-value)ofvoxelswithstatisticalsigniﬁcancewerecal- culatedin83brainregionsbasedonHammersmithatlas.

Tochecksamplehomogeneityineachdataset,weused“checksam- ple homogeneity” fromtheCAT12toolbox(DepartmentsofPsychiatry andNeurology,JenaUniversityHospital,Germany)embeddedwithin SPM12.Thistoolusesameancorrelationofeachimageasameasure ofhomogeneitytoidentifyoutlierimagesinasample.Accordingly,the correlationiscomputedbetweenallimagesacrossthesampleandthe meanforeveryimageiscalculated.Afterwards,aviolinplotwasused tovisualizethefrequencydistributionofthemeancorrelationineach imaginggroupseparately.

3. Results

Overall,theachievedimagequalityusingdeeplearningapproaches bothinimagespaceandprojectionspacewasalmostsimilartoground truthFDimages,deﬁnitelyoutperformingLDimages.Transverse,coro- nal,andsagittalviewsof brainimagesandtheir correspondingbias mapsforFD,LD,IS,andSSofapatientwithalargebiasbetweenLD andFDweredepictedinFig.2.Theinspectionofintensityproﬁlesre- vealedthatthebrainanatomy,especiallygyrusstructuresandradioac- tiveuptakepatterns,aresharperandaremoreobservableanddistin- guishableonimagesreconstructedfrompredictedTOFsinograms(SS) 4

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Fig.3. Jointhistogramsanalysisoflow-dose image (left)and predictedimages in image space(middle)andpredictedfull-doseinsino- gramspace(right)versusstandarddoseimage servingasreference.

Table2

Statisticalanalysisofimagequalitymetricsforlowdoseimages, testpredictedimagesinsinogramandimagespace.SSIMstruc- turalsimilarityindexmetrics,PSNR,peaksignaltonoiseratio, RMSE,rootmeansquarederror.

Test dataset SSIM PSNR RMSE

Low-dose (LD) 0.86 ± 0.02 31.12 ± 0.22 0.35 ± 0.06 Image Space (IS) 0.97 ± 0.01 33.70 ± 0.32 0.17 ± 0.03 Sinogram Space (SS) 0.98 ± 0.01 39.36 ± 0.21 0.14 ± 0.09 P-value (IS vs. SS) 0.041 0.046 0.038 P-value (IS vs. LD) 0.023 0.032 0.022 P-value (SS vs. LD) 0.016 0.028 0.019

Table3

ThepercentageofaverageandabsoluteaverageofSUVbiasandstan- darddeviationforLD,IS,SSforallregions.

LD IS SS

Average SUV bias 0.17 ± 1.96 0.98 ± 1.34 0.22 ± 1.77 Absolute average for SUV bias 1.59 ± 1.03 1.40 ± 0.72 0.96 ± 0.95

relativetothosepredictedinimagespace(IS).Thisvisioninspection wassupportedbyqualitymetricsincludePSNR,SSIM,andRMSEwere calculatedbetweenFDandLD,IS,andSSinTable2.Thenoisedegrada- tionandqualityenhancementofthemodelweretrainedwithsinogram issigniﬁcantlyhigherthanthemodelwastrainedinimagesspace.

Intermsofquantitativeaccuracy,theaverageandabsoluteaverage SUVbiasinallregionsforLD,ISandSSareshowninTable3.Ourre- sultsshowthatthelowestabsoluteaverageSUVbias(0.96±0.95%) wasachievedforSSacrossallthe83regionswhileISandLDshowed anabsoluteaverageSUVbiasof1.40±0.72%and1.59±1.03%,respectively.

Thepixel-wiselinearregressionanalysisof¹⁸F-FDGtraceruptake forLD,ISandSSwithrespecttoFDimageswasillustratedinFig.3. ThescatterofthedatapointsdecreasesfromLDtoISandthenSSand thecorrelationincreasedforIS(R²=0.97,MSE=0.028)comparedto LD(R²=0.94,MSE=0.122).Yet,thehighestcorrelationandlowest scatterwereachievedbySS(R²=0.99,MSE=0.019).

TheMountainandBland&AltmanplotswereshowninFig.4,re- flectingthebiasandvarianceofLDandsynthesizedimagesinthe83 brainregions.Eachorangecirclerepresentsabrainregion.TheMoun- tainplotsindicatethatthetaillengthdecreasessignificantlyinFD– SS plotcomparedwithFD– LDplot.TheBland&Altmanplotsrevealedthat thelowestSUVbias(−0.4%)andminimumvariance(95%CI:−2.6%, +1.9%)wasachievedbypredictedSSimages.AlthoughLDimagesshow alowerSUVbias(0.1%),thevarianceishigh(95%CI:−3.9,+4.1),re- flectingpoorimagequality.TheBland&AltmanandMountainplotsare ingoodagreementwiththejointhistogramanalysisresults.

Table4

ThenumberofvoxelswithsigniﬁcantdiﬀerenceinLD,ISand SScomparedwithFD.Thecorrespondingvolumeandmeant- testvalueareshown.

Number of voxels Volume (mm ³) Mean t-value FD - LD 240,845 1,926,760 10.470031 FD - IS 184,448 1,475,584 7.590589

FD - SS 17,322 138,576 5.888064

Fig.5showstheSUVbiasandSTDof¹⁸F-FDGuptake(TheSTDin- sideeachregion)for83brainregionsextractedfromtheHammersmith brainatlasforLD,IS,andSS.Toreducethenumberofbrainregions, wemergedthesymmetricalleft/rightsidesandreportedtheresultsfor 44insteadof83regions.ThegraphshowedthatthemagnitudeofSUV biasismostlybelow3%forLD,IS,andSS,whileLDshowedahighSTD ineachregioncomparedtoISandSS,reﬂectingahighernoiselevelin LDimages.Moreover,ISpresentedwithahighervariancecomparedto SS.Althoughthelow-doseimagesbearoveralllowSUVbias(owingto zero-meanPoissonnoise),thehighnoiselevelandlocalnoise-induced biasmayimpactclinicalassessment.

Fig.6andTable4depictvoxel-wiset-testanalysisforLD,ISandSS.

Theresultsshowedthattherearevoxelswithsigniﬁcantlylowerval- uesinLD,IS,andSSimagescomparedtoFDimages.However,there werenovoxelswithsigniﬁcantlyhighervaluesinLD,IS,andSSim- ages.Inthiswork,themeant-testwascomputedoverallvoxelsinthe image.Theregion-wiset-testanalysisisshowninSupplementalTable1.

Fig.7showsaViolinplotdepictingthefrequencydistributionofmean correlationbetweenFD,LD,ISandSSimages,separately.

4. Discussion

We evaluatedtheperformanceof adeeplearningmodelfor syn- thesizingdiagnosticqualityFDimagesfromundersampledLDimages corresponding to 5% of the injected radiotracer. We trained seven deep learning modelsseparately to generate FD TOF sinogram bins fromtheircorrespondingLDTOFsinogrambinsandcomparedthere- sultswitha modeltrainedtosynthesize FDimagesfrom LDimages.

Awell-optimized2DResNetDNNwasusedforimage-to-imagetrans- lationandforeach TOFbin separately.Westopped theDNNmodel at thelowesttrainingloss.Our hypothesiswas thatifwesplitare- constructedTOFimageintosevenTOFbinsinogramsandtrainseven independentDNNmodelsforeach,theﬁnalmodelwouldbemoreac- curateandrobustthanasimplemodeloperatinginimagespace.Im- plementationinprojectionspaceinvolvedtheuseofextended/detailed data(400×168×621×7=292′118’400)comparedtoimagespace (101×101×71=724′271).Themodeltrainedinprojectionspace(SS) generatedimageswithhigherimagequalityandlowerabsolutetracer uptakebiasinbrainregionscomparedwithimagessynthesizedinimage

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Fig.4. MountainandBlandAltmanplotofregion-wisestandardizeduptakevaluecomparingFDtoLD,ISandSSimagesacrossalldatasetsforthe83regions.The solidblueanddashedlinesdenotethemeanand95%confidenceinterval(CI)oftheSUVdifferences,respectively.IntheMountainplot,thelongtailsreflectlarge differencesbetweenthemethods.Formodelswithlowerbias,themountainwillbecenteredoverzero.

space(IS).Thisconfirmedourhypothesisthattrainingsevenmodelsfor eachTOFsinogrambinseparatelyleadstoabetterperformancecom- paredtoasinglemodelimplementationinimagespace.Wereducedthe complexityoftheproblembysplitting theTOFsinogramsintoseven separateTOFbinsfollowedbytrainingamodelforeachbin.Moreover, asdifferentTOFbinscontaindifferentsignalandnoisedistributions,in- dependentimplementationsofdenoisingnetworkswouldleadtomore accuratemodelingofsignalandnoiseineach TOFbin.InbrainPET imaging,sincetheheadiscommonlypositionedinthecenteroftheFOV, thecentralTOFbinscontainstrongersignalsandareconsequentlychar- acterizedbyhigherSNR.Conversely,off-centerTOFbinswouldcontain lesscounts/signalandconsequentlyhavelowerSNR.Inthislight,imple- mentationofindependentdenoisingnetworksforeachTOFbinwould moreaccuratelymodelthenoisedistributionassociatedwitheachTOF bin.AmodelcombiningallTOFbinswouldleadtooverestimationor underestimationofnoiseincertainTOFbins.

Overall,bytrainingseveralmodelsforthediﬀerentTOFbins,theef- fectofmotioncanbereduced,particularlyinwhole-bodyPETimaging.

Trainingseparatemodelsforeachtimebinlimitstheeﬀectofmotion toonlyonetimebinandpreventsspreadingittoallTOFbins(e.g.mo- tionofpartofpatient’sbody,suchasonearm).Thisstrategyhelpsto decreasemotionblurcomparedtotrainingasinglemodelforallbinsor eventrainingofnon-TOFsinograms.

Comparisonoftheresultspresentedinthisworktopreviousstudies shouldtake intoconsiderationsomeimportantfactors,suchasscan- ning time, injected dose, the time between injection and scanning, scannersensitivityandcount-rateperformanceanddatapreparation.

Ouyangetal.(2019) proposedaDNNmodelforsynthesizingFDim- agesfromLDimageswith1%of thefull-dose alongwiththree MRI sequences.TheyreportedaSSIMof0.98(comparedwith0.97and0.98 forISandSS,respectively)andRMSEof0.14(comparedto0.17and 0.14forISandSS,respectively).Itisworthemphasizingthatalthough theyusedLDimageswithﬁvetimeslowerdosepercentagerelativeto ourstudy,thesensitivityoftheirPETscanner(GESIGNAPET/MRI)was substantiallyhigher(morethan2timeshighersensitivitythanourBi- ographmCT).Inaddition,theamountofradiotracerinjectedtotheir

patientswas substantiallyhigher(330±30 MBqvs205 ±10 MBq) andtheyalsoincorporatedco-registeredMRimagesassupport.Com- paredtoourpreviousworkwherewefocusedonnon-TOF(Sanaatetal., 2020),thisworkdemonstratedthataddingTOFinformationimproves thequalityofLDandFDimages,whichcanleadtofasterconvergence ofmodelstrainedeitherintheimageorsinogramdomain.Conversely, trainingseveralDNNmodelsforeachtimebincanaddextraerrorin eachpredictedbinthatmightcauseerroraccumulationintheﬁnalTOF sinogram.Hence,theprocessofoptimizationandtrainingofthenet- worksiscriticalandcomplex.

Conventional PET image denoising techniques, suchas non-local mean and bilateral filtering, would inevitably cause signal loss and/or uptakebias within thenoise suppressionprocess(Arabi and Zaidi, 2018), particularly in the presence of the high noise levels (ArabiandZaidi,2020).However,deep learning-basedsolutions en- able reliablenoisesuppressionwithout introducingnoticeablesignal lossand/oruptakebias,whichrendersthemsuitableforclinicaladop- tion(Sanaatetal.,2020,2021).Comparisonofvariousdeeplearning architecturesoralgorithmsiscommendedtoachieveareliablemodel enablingeffectivenoisesuppressionwithminimalsignallossorimage artifacts.Thiseffortwarrantsathoroughinvestigationandfallsbeyond thescopeofthisstudy.Nevertheless,implementationofdeeplearning approachesinthesinogramdomainshouldbeseriouslyconsideredsince theyenabledata—drivenselectionofthemostsuitablereconstruction algorithmand/orsettings(ArabiandZaidi,2021).

Thegeneralizabilityandrobustnessofdeeplearningmodelsisan importantfactorthatdeterminestowhatdegreethemodel’soutputare trustableandrobustwhentestingwithnewnormal/abnormalunseen datasets.Weusedaheterogeneousdatasetconsistingofbothhealthy andabnormalpatientswithvarioustypesofneurodegenerativedisor- ders. Voxel-wise analysisevaluatedeach voxelin allimages(LD,IS, andSS)comparedtoFDimagestodeterminewhetherthere isasta- tisticallysignificantdifferenceatthevoxellevel.Thisapproachoffers anoverallaccuracymeasureofthemodelforaccuratepredictionin- dependent of subjects’ healthcondition. Therefore,modelswithless significantlydifferentvoxelswouldbemoresimilartoFDimagesand 6

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Fig.5. TheSUVbiasrelativetoFDimagesandstandarddeviationforLD,IS,SSandFD.Tomaketheplotmorereadable,wereporttheaverageofleftandright regions(44regions).

viceversa.ThisanalysisrevealedthattheSS modelismoreaccurate thantheISmodel.However,thenumberofvoxelswithsigniﬁcantdif- ferencewerelowerinbothISandSSmodelsthanthatinLDimages.

Hence,thereismoresimilaritybetweenthepredictedmodels(ISand SS)andFDgroupthanbetween LDgroupandFDgroup. Moreover, voxel-wisestatisticalanalysisenabledtoquantifythenumberofvox- elswithsigniﬁcantdiﬀerences in variousregionsof thebraininthe predictedimages(ISandSS)comparedtoFDimages(supplementary Table1).

TheMountainandBland-Altmananalysisrevealedthatthemodel trainedinprojectionspaceledtolowerbiasandvariancerelativetoim- agespace.IntheMountainplot,themedianofthediﬀerencesiscloseto zeroforLDandthenshifttoleftforISandSS,reﬂectingtheoverestima- tionoftraceruptakeofbothmodels.Theshortertailswereobservedfor

SS,IS,andLDimages,respectively,demonstratingthelevelofdiﬀerence withreferenceFDimages.

OneofthedrawbacksofthepresentstudywasthattheLDimages wereproducedbyrandom undersamplingthelist-modedatainstead of re-injectingthepatientwith5%of theamount ofradiotracerand rescanning.AnotherlimitationoforworkisthelimitedsizeofGPU’s RAM whichpreventedtrainingthemodelusingthewholeTOFsino- gramsimultaneously.Inaddition,patientmotionspatiallyforpediatric andelderlypatientswhosuﬀerfromdementiamayleadtoamismatch betweenCTandPETimagesandcausetheimagequalitydegradation forbothLDandFDPETimages.Trainingthemodelin2Disanother limitationofthiswork.Extensionofthesameapproachforwholebody imagingwouldbetime-consumingandifseparatemodelsaretrained foreachsinogrambin.

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Fig.6. 3D-renderedviewsofvoxel-wiseanalysisofLD (a),IS(b),andSS(c)imagesincomparisonwithorigi- nalFDimages.Theimagesdepictregionaldifferences inthreeimagegroups(LD,ISS,andSS)comparedwith FDimages.Theredregionsrepresentvoxelswithsig- nificantdifference,whilewhiteregionsindicatevoxels withoutsignificantdifference.

Fig.7.ViolinplotofthemeancorrelationFD,LD(leftpanel),IS(middelpanel),andSS(rightpanel).Theviolinplotdepictsthefrequencydistributionofmean correlationindiﬀerentimages.Thedistributionpatternofthedataisconsideredasthesimilaritymeasureinordertoassessthelevelofdiﬀerencebetweengroups.

Inaddition,itcanberegardedasameasuretoevaluatetheaccuracyofmodels’prediction.Accordingtothisplot,theSSmodeloﬀersahigheraccuracycompared toISmodelforpredictinggroundtruthFDimagescorrectly.

5. Conclusion

WedemonstratedthattrainingseparateResNetalgorithmsformap- pingtheLDTOFsinogrambinstotheircorrespondingFDTOFsinogram binsenablestogeneratehigh-quality¹⁸F-FDGbrainPETimages.There- sultsrevealedthesuperiorperformanceoftheTOFmodelimplemented inprojectionspacecomparedtotheimplementationinimagespace.The predictedimagesinprojectionspaceledtobetternoisecharacteristics andoveralllowerabsolutetraceruptakebias.

Dataandcodeavailabilitystatement

TheMatLab/Pythoncodeisavailablefromtheauthorsuponrequest.

Creditauthorshipcontributionstatement

Amirhossein Sanaat: Conceptualization, Methodology, Software, Writing– review&editing,Writing– originaldraft.HosseinShooli:

Datacuration, Writing – review & editing, Writing – original draft, Methodology.SohrabFerdowsi:Conceptualization,Writing– review&

editing,Writing– originaldraft.IsaacShiri:Conceptualization,Writing

– review&editing,Writing– originaldraft.HosseinArabi:Conceptu- alization,Writing– review&editing,Writing– originaldraft.Habib Zaidi:Writing– review&editing,Writing– originaldraft,Methodol- ogy,Conceptualization.

Acknowledgments

ThisworkwassupportedbytheSwissNationalScienceFoundation undergrantSNRF320030_176052,theEurostarsprogram oftheEu- ropeancommissionundergrantE!114021ProVisionandthePrivate FoundationofGenevaUniversityHospitalsunderGrantRC-06–01.

Supplementarymaterials

Supplementarymaterialassociatedwiththisarticlecanbefound,in theonlineversion,atdoi:10.1016/j.neuroimage.2021.118697.

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